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A. V. Titov

Publications and source records attributed to A. V. Titov.

At least 37 records · Page 2Linked to original sources
arXiv2017

Zeeman interaction in $^3Δ_1$ state of HfF$^+$ to search for the electron electric-dipole-moment

We report the theoretical investigation of the suppression of magnetic systematic effects in HfF$^+$ cation for the experiment to search for the electron electric dipole moment. The g-factors for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Δ_1$ state are calculated as functions of the external electric field. The lowest value for the difference between the g-factors of $Ω$-doublet levels, $Δg = 3 \times 10^{-6}$, is attained at the electric field 7 V/cm. The body-fixed g-factor, $G_{\parallel}$, was obtained both within the electronic structure calculations and with our fit of the experimental data from [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science {\bf 342}, 1220 (2013)]. For the electronic structure calculations we used a combined scheme to perform correlation calculations of HfF$^+$ which includes both the direct 4-component all-electron and generalized relativistic effective core potential approaches. The electron correlation effects were treated using the coupled cluster methods. The calculated value $G_{\parallel}=0.0115$ agrees very well with the $G_{\parallel}=0.0118$ obtained in the our fitting procedure. The calculated value $D_{\parallel}=-1.53$ a.u. of the molecule frame dipole moment (with the origin in the center of mass) is in agreement with the experimental value $D_{\parallel}=-1.54(1)$ a.u. [H. Loh, Ph.D. thesis, Massachusetts Institute of Technology (2006)].

physics.atom-ph↗
arXiv2017

Enhanced effect of CP-violating nuclear magnetic quadrupole moment in HfF$^+$ molecule

HfF$^+$ cation is a very promising system to search for the electron electric dipole moment (EDM), and corresponding experiment is carried out by E. Cornell group. Here we theoretically investigate the cation to search for another T,P-odd effect -- the nuclear magnetic quadrpole moment (MQM) interaction with electrons. We report the first accurate ab initio relativistic electronic structure calculations of the molecular parameter $W_M$=0.494 $\frac{10^{33}\mathrm{Hz}}{e~{\rm cm}^2}$ that is required to interpret the experimental data in terms of the MQM of Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes, CCSDT(Q). We discuss interpretation of the MQM effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $θ$ and quark chromo-EDM.

physics.atom-ph↗
arXiv2016

Renormalisation Group Corrections to Neutrino Mixing Sum Rules

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\tilde{U}_ν$, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $δ$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of $\tilde{U}_ν$. We consider five extensively discussed possible symmetry forms of $\tilde{U}_ν$: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for $δ$ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.

hep-ph↗
arXiv2016

Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay

We obtain predictions for the Majorana phases $α_{21}/2$ and $α_{31}/2$ of the $3\times 3$ unitary neutrino mixing matrix $U = U_e^{\dagger} \, U_ν$, $U_e$ and $U_ν$ being the $3\times 3$ unitary matrices resulting from the diagonalisation of the charged lepton and neutrino Majorana mass matrices, respectively. We focus on forms of $U_e$ and $U_ν$ permitting to express $α_{21}/2$ and $α_{31}/2$ in terms of the Dirac phase $δ$ and the three neutrino mixing angles of the standard parametrisation of $U$, and the angles and the two Majorana-like phases $ξ_{21}/2$ and $ξ_{31}/2$ present, in general, in $U_ν$. The concrete forms of $U_ν$ considered are fixed by, or associated with, symmetries (tri-bimaximal, bimaximal, etc.), so that the angles in $U_ν$ are fixed. For each of these forms and forms of $U_e$ that allow to reproduce the measured values of the three neutrino mixing angles $θ_{12}$, $θ_{23}$ and $θ_{13}$, we derive predictions for phase differences $(α_{21}/2 - ξ_{21}/2)$, $(α_{31}/2 - ξ_{31}/2)$, etc., which are completely determined by the values of the mixing angles. We show that the requirement of generalised CP invariance of the neutrino Majorana mass term implies $ξ_{21} = 0$ or $π$ and $ξ_{31} = 0$ or $π$. For these values of $ξ_{21}$ and $ξ_{31}$ and the best fit values of $θ_{12}$, $θ_{23}$ and $θ_{13}$, we present predictions for the effective Majorana mass in neutrinoless double beta decay for both neutrino mass spectra with normal and inverted ordering.

hep-ph↗
arXiv2015

Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries

Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group $G_f$, and that $G_f$ is broken to specific residual symmetries $G_e$ and $G_ν$ of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase $δ$ of the neutrino mixing matrix $U$. The residual symmetries considered are: i) $G_e = Z_2$ and $G_ν = Z_n$, $n > 2$ or $Z_n \times Z_m$, $n,m \geq 2$; ii) $G_e = Z_n$, $n > 2$ or $Z_n \times Z_m$, $n,m \geq 2$ and $G_ν = Z_2$; iii) $G_e = Z_2$ and $G_ν = Z_2$; iv) $G_e$ is fully broken and $G_ν = Z_n$, $n > 2$ or $Z_n \times Z_m$, $n,m \geq 2$; and v) $G_e = Z_n$, $n > 2$ or $Z_n \times Z_m$, $n,m \geq 2$ and $G_ν$ is fully broken. For given $G_e$ and $G_ν$, the sum rules for $\cosδ$ thus derived are exact, within the approach employed, and are valid, in particular, for any $G_f$ containing $G_e$ and $G_ν$ as subgroups. We identify the cases when the value of $\cosδ$ cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of $\cosδ$ can be unambiguously predicted once the flavour symmetry $G_f$ is fixed. We present predictions for $\cosδ$ in these cases for the flavour symmetry groups $G_f = S_4$, $A_4$, $T^\prime$ and $A_5$, requiring that the measured values of the 3-neutrino mixing parameters $\sin^2θ_{12}$, $\sin^2θ_{13}$ and $\sin^2θ_{23}$, taking into account their respective $3σ$ uncertainties, are successfully reproduced.

hep-ph↗
arXiv2015

Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis

We derive predictions for the Dirac phase $δ$ present in the $3\times 3$ unitary neutrino mixing matrix $U = U_e^{\dagger} \, U_ν$, where $U_e$ and $U_ν$ are $3\times 3$ unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices. We consider forms of $U_e$ and $U_ν$ allowing us to express $δ$ as a function of three neutrino mixing angles, present in $U$, and the angles contained in $U_ν$. We consider several forms of $U_ν$ determined by, or associated with, symmetries, tri-bimaximal, bimaximal, etc., for which the angles in $U_ν$ are fixed. For each of these forms and forms of $U_e$ allowing one to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for $\cos δ$, using i) the latest results of the global fit analysis of neutrino oscillation data, and ii) the prospective sensitivities on the neutrino mixing angles. Our results, in particular, confirm the conclusion, reached in earlier similar studies, that the measurement of the Dirac phase in the neutrino mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information as regards the possible existence of symmetry in the lepton sector.

hep-ph↗
arXiv2015

TaN molecule as a candidate to search for New physics

It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $θ$ and quark chromo-EDM.

physics.atom-ph↗
arXiv2015

Verification of g-factors for lead monofluoride ground state, PbF

We report the results of our theoretical study and analysis of earlier experimental data for the g-factor tensor components of the ground $^2Π_{1/2}$ state of free PbF radical. The values obtained both within the relativistic coupled-cluster method combined with the generalized relativistic effective core potential approach and with our fit of the experimental data from [R.J. Mawhorter, B.S. Murphy, A.L. Baum, T.J. Sears, T. Yang, P.M. Rupasinghe, C.P. McRaven, N.E. Shafer-Ray, L.D. Alphei, J.-U. Grabow, Phys. Rev. A 84, 022508 (2011); A. Baum, B.S. thesis, Pomona College, 2011]. The obtained results agree very well with each other but contradict the previous fit performed in the cited works. Our final prediction for g-factors is $G_{\parallel}= 0.081(5)$, $G_{\perp}=-0.27(1)$.

physics.atom-ph↗
arXiv2015

Theoretical study of ThF$^+$ in the search for T,P-violation effects: Effective state of a Th atom in ThF$^+$ and ThO compounds

We report the results of theoretical investigation of electronic structure of ThF$^+$ cation which is one of the most interesting systems to search for the electron electric dipole moment (eEDM) [H. Loh, K.C. Cossel, M.C. Grau, K.-K. Ni, E.R. Meyer, J.L. Bohn, J. Ye, E.A. Cornell, Science {\bf 342}, 1220 (2013)] and other effects of violation of time reversal (T) and spacial parity (P) symmetries in fundamental interactions. For the working $^3Δ_1$ state we have found a quite high value of the effective electric field acting on unpaired electrons (37.3 GV/cm). The field will be required to interpret the experiment planed on ThF$^+$ in terms of eEDM. Within the concept of atoms in compounds [A.V. Titov, Y.V. Lomachuk, and L.V. Skripnikov, Phys. Rev. A {\bf 90}, 052522 (2014)] we have compared the ThF$^+$ electronic structure with that of ThO. Also we have calculated other parameters of T,P-odd interactions: $W_{T,P}$, which is needed for interpretation of the experiment in terms of the dimensionless constant $k_{T,P}$ characterizing the strength of the T,P-odd pseudoscalar$-$scalar electron$-$nucleus neutral current interaction (50 kHz); $W_M$, which is required to search for the Th nuclear magnetic quadrupole moment in $^{229}$ThF$^+$ (0.88 $\frac{10^{33}\mathrm{Hz}}{e {\rm cm}^2}$). A number of properties which can be measured are also calculated: hyperfine structure constant, the molecule-frame dipole moment, and g-factor.

physics.atom-ph↗
arXiv2015

Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules

Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_ν$, where $U_{e}$ and $U_ν$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase $δ$ present in $U$ satisfies when $U_ν$ has a form dictated by flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_ν$, so that reactor, atmospheric and solar neutrino mixing angles $θ_{13}$, $θ_{23}$ and $θ_{12}$ have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge $L' = L_e - L_μ- L_τ$ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for $δ$ in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for $\cosδ$ proposed in the literature, taking into account also the uncertainties in the measured values of $\sin^2θ_{12}$, $\sin^2θ_{23}$ and $\sin^2θ_{13}$. This allows us, in particular, to assess the accuracy of the predictions for $\cosδ$ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3$σ$ experimentally allowed ranges.

hep-ph↗
arXiv2015

Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix

Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_ν$, where $U_{e}$ and $U_ν$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the predictions based on the sum rules which the Dirac phase $δ$ present in $U$ satisfies when $U_ν$ has a form dictated by, or associated with, discrete flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_ν$, so that the reactor, atmospheric and solar neutrino mixing angles $θ_{13}$, $θ_{23}$ and $θ_{12}$ have values compatible with the current data.

hep-ph↗
arXiv2014

Towards the search of T,P-odd interactions in lead monofluoride, PbF

The relativistic coupled-clusters method combined with the generalized relativistic effective core potential approach and nonvariational one-center restoration technique is applied to evaluation of parameters of spin-rotational effective Hamiltonian in lead monofluoride to study the effects of violation of time-reversal invariance (T) and space parity (P) in PbF. The obtained hyperfine structure constants, A$_{||}$=9942 MHz and A$_{\perp}$=-7174 MHz are stable with respect to the improvement of the correlation treatment and they are in a very good agreement with the experimental data, A$_{||}$=10147 MHz and A$_{\perp}$=-7264 MHz [PRA {\bf 84}, 022508 (2011)]. This is essential to the important task of verifying the value of effective electric field \Eeff =40 GV/cm, the parameter of P-odd interaction $W_{P}$=-1213 Hz and the parameter of T,P-odd pseudoscalar$-$scalar electron$-$nucleus interaction $W_{T,P}$=91 kHz, which are of primary interest in the paper.

physics.atom-ph↗
arXiv2014

Theoretical study of thorium monoxide for the electron electric dipole moment search, II: Electronic properties of $H^3Δ_1$ in ThO

Recently an improved limits on the electron electric dipole moment, \eEDM, and dimensionless constant, $k_{T,P}$, characterizing the strength of the T,P-odd pseudoscalar$-$scalar electron$-$nucleus neutral current interaction in the $H^3Δ_1$ state of ThO molecule were obtained by ACME collaboration [Science 343, 269 (2014)]. The interpretation of the experiment in terms of fundamental quantities \eEDM\ and $k_{T,P}$ is based on the results of theoretical study of appropriate ThO characteristics, the effective electric field acting on electron, \Eeff, and a parameter of the T,P-odd pseudoscalar$-$scalar interaction, $W_{T,P}$, given in [J.Chem.Phys.\ 139, 221103 (2013)] by St.Petersburg group. To reduce the uncertainties of the given limits we report improved calculations of the molecular state$-$specific quantities \Eeff, 81.5~GV/cm, and $W_{T,P}$, 112~kHz, with the uncertainty within 7\% of the magnitudes. Thus, the values recommended to use for the upper limits of the quantities are 75.8~GV/cm and 104~kHz, correspondingly. The hyperfine structure constant, molecule-frame dipole moment of the $H^3Δ_1$ state and $H^3Δ_1\to X^1Σ^+$ transition energy which, in general, can serve as a measure of reliability of the obtained \Eeff\ and $W_{T,P}$ values are also calculated. Besides we report the first calculation of g-factor for the $H^3Δ_1$ state of ThO. The results are compared to the earlier experimental and theoretical studies, and a detailed analysis of uncertainties of the calculations is given.

physics.atom-ph↗
arXiv2014

Calculation of the parity and time reversal violating interaction in ^{225}RaO

The 10-electron generalized relativistic effective core potential and the corresponding correlation spin-orbital basis sets are generated for the Ra atom and the relativistic coupled cluster calculations for the RaO molecule are performed. The main goal of the study is to evaluate the P,T-odd parameter X characterized by the molecular electronic structure and corresponding to a "volume effect" in the interaction of the ^{225}Ra nucleus Schiff moment with electronic shells of RaO. Our final result for X(^{225}RaO) is -7532 which is surprisingly close to that in ^{205}TlF but has different sign. The obtained results are discussed and the quality of the calculations is analyzed. The value is of interest for a proposed experiment on RaO [PRA 77, 024501 (2008)] due to a very large expected Schiff moment of the ^{225}Ra nucleus.

physics.atom-ph↗
arXiv2014

Ab initio study of radium monofluoride, RaF, as a candidate to search for P- and T,P- violation effects

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T,P-violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the ${^2}Σ$ electronic ground state of RaF molecule. They include the parameter $W_a$, which is critical in experimental search for nuclear anapole moment and the parameters $W_d$ and $W_{\rm SP}$ required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter $X$ corresponding to the "volume effect" in the T,P$-$odd interaction of the $^{223}$Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for $^{223}$RaF and $^{223}$Ra$^+$ have been computed as well, demonstrating the accuracy of the methods employed.

physics.atom-ph↗
arXiv2014

Manifestations of nuclear CP-violation in ThO molecule

Investigations of CP violation in hadron sector may be done using measurements in the ThO molecule. Recent measurements in this molecule improved the limit on electron EDM by an order of magnitude. Another time reversal (T) and parity (P) violating effect in $^{229}$ThO is induced by the nuclear magnetic quadrupole moment. We have performed nuclear and molecular calculations to express this effect in terms of the strength constants of T,P-odd nuclear forces, neutron EDM, QCD vacuum angle $θ$, quark EDM and chromo-EDM.

physics.atom-ph↗
arXiv2014

Zeeman interaction in ThO $H^3Δ_1$ for the electron EDM search

The current limit on the electron's electric dipole moment, $|d_\mathrm{e}|<8.7\times 10^{-29} e {\cdotp} {\rm cm}$ (90% confidence), was set using the molecule thorium monoxide (ThO) in the $J=1$ rotational level of its $H ^3Δ_1$ electronic state [Science $\bf 343$, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its $Ω$-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the $g$-factor difference between the $Ω$-doublets is minimized. We consider the $g$-factors of the ThO $H^3Δ_1$ state both experimentally and theoretically, including dependence on $Ω$-doublets, rotational level, and external electric field. The calculated and measured values are in good agreement. We find that the $g$-factor difference between $Ω$-doublets is smaller in $J=2$ than in $J=1$, and reaches zero at an experimentally accessible electric field. This means that the $H,J=2$ state should be even more robust against a number of systematic errors compared to $H,J=1$.

physics.atom-ph↗